Start by combining the milk and sugar in a medium saucepan over medium heat. Stir occasionally until the sugar dissolves completely and the milk is warm but not boiling.
In a separate bowl, whisk together the fine semolina and cornstarch. This mixture will thicken the custard and give it a smooth texture.
Beat the egg lightly in another bowl. Gradually add a small amount of the warm milk mixture to the egg while whisking constantly to temper it and prevent scrambling.
Slowly pour the tempered egg back into the saucepan with the warm milk and sugar mixture. Add the semolina and cornstarch mixture in small increments, whisking constantly to avoid lumps.
Continue to cook over low heat, stirring constantly until the custard thickens to a creamy consistency, about 5-7 minutes.
Remove the pan from heat. Stir in the butter, vanilla extract, and freshly grated lemon zest until fully incorporated and smooth.
Roll out the all butter pie crust dough evenly and gently place it into your pie dish, trimming any excess edges.
Pour the warm custard filling into the prepared crust, smoothing the top with a spatula. Beat the half egg with 10 ml milk and brush the crust edges to achieve a golden brown finish.
Preheat your oven to 180°C (350°F) and bake the pie for about 40-45 minutes, or until the custard is set and the crust is golden.
Allow the pie to cool completely at room temperature. This cooling step lets the custard set fully, making it easier to slice and enjoy.